Incorporating Graphical Structure of Predictors in Sparse Quantile Regression

Zhanfeng Wang, Xianhui Liu, Wenlu Tang, Yuanyuan Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

Quantile regression in high-dimensional settings is useful in analyzing high-dimensional heterogeneous data. In this article, different from existing methods in quantile regression which treat all the predictors equally with the same priori, we take advantage of the graphical structure among predictors to improve the performance of parameter estimation, model selection, and prediction in sparse quantile regression. It is shown under mild conditions that the proposed method enjoys the model selection consistency and the oracle properties. An alternating direction method of multipliers algorithm with a linearization technique is proposed to implement the proposed method numerically, and its convergence is justified. Simulation studies are conducted, showing that the proposed method is superior to existing methods in terms of estimation accuracy and predictive power. The proposed method is also applied to a real dataset.

Original languageEnglish
Pages (from-to)783-792
Number of pages10
JournalJournal of Business and Economic Statistics
Volume39
Issue number3
DOIs
Publication statusPublished - Jul 2021
Externally publishedYes

Keywords

  • ADMM algorithm
  • Graphical structure
  • Quantile regression
  • Sparse regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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